Query on Bucholz Tie break system for Swiss Chess Tourneys!

Hi friends,

I understand that Bucholz system (where sum of all opponent's scores are added up to get a player's score) is one of the most effective and widely used Tie break system in Swiss Chess Tournaments.

My doubt is, say in a 8 round Swiss Tournament, what happens if 2 players I met in rounds 2 and 3 withdraw from the rest of the tourney from round 4?

How will this be taken into account while calculating my Bucholz score? Because it is obvious that such a player will lose out if the sum of all players are considered because 2 of the opponents wouldnt have scored for 5 rounds!

Is there any rule or something in FIDE/USCF to factor this?

Any suggestions/opinions will be very helpful.

Thanks and Regards,

Arun

I've never thought about that. It seems like a good question.

I think that if they have played less than half their games, their results are stricken from the record.  Perhaps you get a point for a bye, but a low tiebreak score.  Fischer withdrawing from Sousse Interzonal in 1967 is a famous example of a player who withdrew, although that was not a Swiss.

I found the relevant passage in the FIDE Handbook:

"Handling of unplayed games for calculation of Buchholz (Congress 2009)
There are two points of view:

1. for the player himself who gets a result by default or is absent
   A virtual opponent of the player is used to calculate the Buchholz of the player. A virtual  opponent has the same points at the beginning of the round and the result by default of a player is treated as a normal result, so a loss by default (or absence) is a win for the virtual opponent and vice versa. For each next round the virtual opponent gains half a point. 
2. for the opponents in other rounds of the player who gets a result by default
   For reducing the consequence for the opponents when calculating Buchholz, each result By default of a player is counted as a half point (draw) for the Buchholz of the player’s opponents."

Another correction from the FIDE handbook:

"If a player withdraws from a Swiss-system tournament the points scored by him and by his opponents shall remain in the cross-table for ranking purposes. Only games that are actually played are rated."